A cuboid has edge 7 centimetres, 5 centimetres and a total surface area of 142 centimetres squared. A larger, similar cuboid has a shortest edge of 12 centimetres. Find the third edge of the smaller cuboid and the volume of the larger cuboid.

Let's call the length of the third edge "Y" so we have edges of 7cm, 5cm and Ycm.There are 6 faces but opposite faces are the same, so there are 3 pairs of faces which are 5cm by 7cm, 5cm by Ycm and 7 by Ycm.The total surface area is therefore 7x5x2 + 7xYx2 + 5xYx2 = 142.
70 + 14Y + 10Y = 142(collect all the Ys)70 + 24Y = 142(subtract 70 from both sides)24Y = 72(divide by 24)Y = 3.
The larger cuboid's smallest edge is 12cm compared with 3cm for the smaller cuboid.The length scale factor will be 12 divided by 3 = 4.The other edges of the cuboid will be 4 x length, so we have edges 4 x 5 = 20cm and 4 x 7 = 28cm.Volume = length x width x height = 12 x 20 x 28 = 6720 centimetres cubed.